Modeling joint patterns using combinations of mechanical and probabilistic concepts

Abstract

Rock fracture pattern description is important in civil engineering, engineering geology, and petroleum engineering. Deformability, strength, and stability of a rock mass as well as fluid flow through it are all influenced by fractures. Rock fracture patterns normally cannot be observed completely so different approaches have been used to model them. Geometric models, which use probabilistic processes usually not or only indirectly related to mechanics, are often used for this purpose. Mechanics-based models, on the other hand, can only describe simpler fracture patterns. This research will improve on fracture pattern modeling capabilities, specifically for layer-perpendicular joints in sedimentary rock. Layer-perpendicular joints in sedimentary rock represent relatively simple fracture patterns that are usually confined within a competent layer bounded by ductile non-jointing layers. Field and laboratory studies in the literature suggest that their spacing is related to layer thickness and follows some probability distribution. Laboratory results in the literature also suggest that for a given layer thickness, a limiting joint spacing exists (i.e., joint saturation); this is not apparent in field data.

(cont.) Existing models for layer-perpendicular joints in sedimentary rock consider some but not all of these aspects. Two new models are developed to better consider them. The first model (flaw model) is mechanics-based and relies on tensile stress and tensile strength submodels to generate joint patterns. Tensile strength can be correlated or uncorrelated. Compressive stress and interface slip saturation mechanisms are also implemented. The second model (rejection procedure) is a faster and largely probabilistic approach that generates joint patterns from a continuously updated probability density function but this function is assumed to depend only on tensile stress. For this reason, the flaw model must always be used to evaluate rejection procedure results. Only the compressive stress saturation is considered in the rejection procedure. Comparisons with field data indicate that both models can produce realistic joint patterns except where there are through-going joints or where strike varies considerably. Also, results indicate that saturation does not always occur in the field. Additionally, it is found that the use of an uncorrelated submodel in the flaw model is adequate for producing realistic joint patterns.